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**NETWORK>COHESION>E-I INDEX**

**PURPOSE **Calculate the E-I index of a partition of a network and perform a permutation test to evaluate its significance.

**DESCRIPTION **Given a partition of a network into a number of mutually exclusive groups then the E-I index is the number of ties external to the groups minus the number of ties that are internal to the group divided by the total number of ties. This value can range from 1 to -1, but for a given network density and group sizes its range may be restricted and so it can be rescaled. The index is also calculated for each group and for each individual actor. A permutation test is performed to see whether the network E-I index is significantly higher or lower than expected. Edge values are ignored.

**PARAMETERS**

** Input Dataset**

* *Name of UCINET dataset to analyzed. Data type: Graph.

**Attribute**

** **The name of an UCINET dataset that contains a partition of the actors. To partition the data matrix into groups specify a vector by giving the dataset name, a dimension (either row or column) and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to define the groups. All actors with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same group.

**Number of random perms:** (Default= 10000)

Number of permutations used in the permutation test.

**Diagonal Values Valid **(Default = 'NO')

Whether to include the diagonal values.

**Random Number Seed**

The random number seed sets off the random permutations. UCINET generates a different random number as default each time it is run. This number should be changed if the user wishes to repeat an analysis. The range is 1 to 32000.

**Output Dataset **(Default = IndE-I)

Name of UCINET file that contains the E-I index for each individual actor.

** **

**LOG FILE **Recoding of the attribute vector used to partition the dataset followed by a blocked density matrix corresponding to the groups.

A table which gives the whole network results, these include the frequencies in the observed data followed by a column that gives these frequencies as a percentage of the total number of ties in the data, the third column gives the maximum possible given the group sizes, the final column headed density gives the observed divided by the maximum possible for the internal and external ties with the final entry in the E-I column giving the value of the E-I index if all the observed ties had been evenly spread within and between the groups ie the expected value. The important values from the table are then reproduced together with the rescaled E-I index.

The results of the permutation test are presented in a table. The observed values are repeated in column 1, the next 4 cols give the minimum, mean, maximum and standard deviation derived from the permutation test. This is followed by the number of times the random test obtains a value greater than or equal to the observed and less than or equal to the observed. This are expressed as a probability and can be used as p values.

A table with the group level ties and E-I index.

Finally a table with the individual ties and E-I index.

**TIMING **O(N)

**COMMENTS **To just calculate the overall E-I index with no permutation test run NETWORK>COHESION>HOMOPHILY

**REFERENCES **Krackhardt, David and Robert N. Stern (1988). Informal networks and organizational crises: an experimental simulation. Social Psychology Quarterly 51(2), 123-140.